This randomized phase II trial studies how well vinorelbine tartrate and cyclophosphamide work in combination with bevacizumab or temsirolimus in treating patients with recurrent or refractory rhabdomyosarcoma. Drugs used in chemotherapy, such as vinorelbine tartrate and cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Bevacizumab may also stop the growth of rhabdomyosarcoma by blocking blood flow to the tumor. Temsirolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether combination chemotherapy is more effective when given together with bevacizumab or temsirolimus in treating rhabdomyosarcoma.